A system like that helps me to know the general vibe of the character and other characters to liken them to (e.g., "Chaotic Good" includes characters like Robin Hood but also 1984's Winston), although of course it's quite limited.

I wonder - are there other easy grids like that which allow me to differentiate between different stereotypes and opposite character traits?

Cool question! This has the potential to turn into a list question, so answerers, please try to post more than simple links to arbitrary grids. @what 's answer below is an excellent example, giving different examples and pointing out some strengths of each one.
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Standback♦May 26 '14 at 6:47

Forgive me if I'm missing the point here, but isn't this more of a gaming question or a design question than a writing question?
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Neil Fein♦May 28 '14 at 2:04

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@NeilFein That's not the intention, although I'm not sure if the wording is clear enough. This is specifically an attempt to find categorizations/stereotypes either as a starting point for a character or as a way to populate the novel with a few side characters. I'm looking at it as a tool to help imagine the characters. For me, if someone says "Chaotic Good" I immediately imagine a certain "vibe" which gives me a few starting points from where I can flesh out the character.
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Michael StumMay 28 '14 at 3:15

@NeilFein I also want to see what are commonly seen as opposites - D&D has "Lawful" and "Chaotic", Myers-Briggs has Sensing vs Feeling (among others) - those types of charts.
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Michael StumMay 28 '14 at 3:19

2 Answers
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From the beginnings of time, scholars have attempted to categorize human character (as well as body type, race, and so on). Most such theories have been shown to bear no relation to reality, but for character building they are as good or better as the morality based D&D system.

The currently most widely used and accepted general system of measuring personality dimensions is the Five Factor Model of personality traits, also called the "Big 5". There are many, many different systems, most developed for a specific purpose (such as selecting suitable applicants for a certain job), so it would depend on your story which would be most appropriate for you.

In a fantasy world building game, that focusses on crafts (woodworker, hunter, scholar, warrior etc.), Holland's occupational themes (often abbreviated to RIASEC and used in many career choice tests) might be useful.

In a romantic story dealing with relationships and interpersonal interaction, the a variant of the Interpersonal Circumplex will help you understand the relevant aspects of your persons character.

And so on. There are just too many systems to list, much less explain them all, here, but if you are interested in psychology and want to take the time, you can certainly find one or merge several and create your own. Just follow the in-text links and articles listed under "See also" in the Wikipedia article on personality types, to start.

Magic: the Gathering has built its entire platform around the five colors of magic, and each one of them has a very distinct set of characteristics that tell you what color or colors you are. The "Guru" of the "Color Pie" is Mark Rosewater, currently the Lead Designer of Magic, and is often asked on his blog to elaborate on the color identity of various fictional and real figures (usually comic book characters).

White puts value in the group, the community, and its civilization as a whole. White's ultimate goal is peace, harmony, and perfection — a world where everyone gets along and no one seeks to disturb the bonds of unity that White had worked so long to forge. To govern and protect its community, White makes use of and puts value in a number of broad concepts; morality (ethics, grace, truth), order (law, discipline, duty), uniformity (conformity, religion), and structure (government, planning, reason).

Blue

Blue is the color that looks on the world and sees opportunity. For Blue, life is a chance to contemplate oneself, and what is possible, and to bring about the best of both. Blue reasons that if it is to make itself better, it must become capable of everything it could be capable of, for that is to "merely add" to its own capabilities. Blue believes it can't possibly be bad to acquire the potential for any conscious action. Blue decides that it must understand everything; for truly, understanding can only improve one's effectiveness in any task. Since knowledge itself will inform every other decision, Blue forms its principle goal: omniscience, the knowledge of all.

Black

Black is the color of self-indulgence, parasitism, amorality and unfettered desire for power. It believes that the world is made for its taking and that the weak exist to be exploited by the strong. The essence of Black is to see one's own ego1 as so supremely invaluable, that the prospect of enslavement, of subordinating that ego to another, is utterly inadmissible. So, to be in accord with its perceptions and beliefs, Black simply must discard all obligations but to acquire power for itself. It can be no less than the one supreme being who is subordinate to no other, the possessor of all power in the universe - it must become omnipotent.

Red

Above all else, red values freedom of expression. It wants to do what it wants, when it wants, to whom it wants, and nobody can tell it otherwise. It believes that life would be much more fun if everyone stopped caring about rules, laws and personal appearances and just spent their time indulging their desires. This leads into red's other core value: chaos. Red sees order of any kind as pointlessly inhibiting, believing that only through embracing anarchy could everyone really be free to enjoy life to the fullest. Finally, red is the color of immediate action and immediate gratification. If it wants something it will act on its impulses and take it, regardless of the consequences.

Green

Green is the color of nature, growth, interdependence and instinct. It believes that obedience the natural order alone is the best way to exist and thus favors a simplistic way of living in harmony with the rest of the world. This can often lead to it be perceived as a pacifistic color, as it does not seek to make conflict with the other colors as long as they leave it alone and do not disrespect nature. However, it is fierce when it feels threatened and can be predatory and aggressive if its instincts dictate.

Now this isn't exactly a matrix, it's a wheel. And a wheel is really 1 dimensional (if you think about it, it all travels in 1 direction - the spokes aren't really used except to keep the track from collapsing on itself...) This wheel has what are known as "allied" and "enemy" colors. In the order listed, White - Blue - Black - Red - Green - White (with white being repeated because it's a wheel, that goes around... the pattern repeats forever) The two colors that surround a given color are considered allied colors. So Black is considered allies with Blue and Red, and enemies with Green and White. And indeed, the enemy philosophies are often considered conflicting. This is very close to what you're looking for in terms of a "opposite character trait" matrix.

But a person is not always simply Black or White (or Blue or Red or Green!) Here's a couple examples that might help you flesh out how to slot people on the color pie.

Tony Stark (Ironman) - One of the world's greatest inventors, cares deeply about the advancement of science. Clearly Blue. (Note: he's Blue because he CARES, not because HE'S SMART.) But, he has no problem demolishing cities with collateral damage to achieve his goals. This chaotic streak labels him Red as well. Early renditions of him might be considered Black, as he can be considered quite selfish, but this appears to be disappearing over time.

Oliver Queen (The Green Arrow) - Early Oliver could easily be considered Black Green. He is incredibly raw and rugged (even though his Billionaire-playboy alter ego was pretty Red, this changed when he became a superhero and is mostly just for show to divert attention from his true self.) He's also willing to go to just about any extreme to extinguish his enemies and has no concept of mercy. After the death of his friend, he reaches a new sense of honor and enlightenment and decides to actively abolish his Black past and transitions to a more merciful White course of action.

Bruce Wayne (Batman) - Bruce himself is a very Blue White person. His curious nature as a tinkerer and inventor and pushing the limits of technology solidifies himself as Blue (much like Stark), but his motivations are simply to save a widely troubled Gotham City. He wants to eliminate crime and establish order, which is a purly White motivation. However, his persona as Batman appears Black. While he really isn't into slaughtering people (which would eliminate crime, but that's not how he wants to do it) he still instills fear in those criminals. So while he wouldn't actually slaughter them in cold blood, he certainly has no problems making them THINK he would, and using this fear to his advantage. This isn't exactly a Black trait, but it is borderline, and certainly could be characterized as Faux Black.

There exists a world in the Magic universe called Ravnica that has ten guilds, one for each color pair, that also help to characterize one facet of that pair. (This isn't to say that a guild comprises all the characteristic-economy of that color pair, only to serve as one good example.)

The Golgari Swarm - (Green/Black) - A sect emphasizing that death is an essential part of life, and that death and plague fosters regrowth and endurance.

The Selensya Conclave (White/Green) - Zealous defenders of keeping life in balance, they hold true to the axiom that the needs of the many outweigh the needs of the few.

House Dimir (Blue/Black) - A network of assassins and spies, most common folk don't believe it even exists. "There are nine guilds" was a popular meme for some time (especially considering the other 9 guilds can be mapped to the 3x3 DnD alignment matrix).

The Orzhov Syndicate (Black/white) - Religion in the front, mafia in the back, these extortionists control most of the spiritual and economic goings-on of the entire planet.

The Izzet League (Blue/Red) - While their inventions keep the Ravnican technosphere afloat, they are more like mad scientists who have caused more than one fatal explosion.

The Gruul Clans (Red/Green) - Not so much a guild anymore due to their savage nature, these clansman represent those who live outside the comforts of the world-spanning city that is Ravnica.

The Azorius Senate (Blue/White) - The lawmakers of Ravnica, they protect the status quo at all costs. Their Blue comes from their pursuit of knowledge, which is immensely useful in politics.

The Cult of Rakdos (Red/Black) - Just your every-day ritualistic-torturing, demon worshipping, murderous cult. Death isn't the objective, it's merely the end of the road of their true goal, torture and pain. I recommend politely declining party invites.

The Simic Combine (Green/Blue) - Originally, the Simic wanted to protect the ever-shrinking natural population as the world-spanning city took over mile after mile of land. As resources dwindle, they must get more creative to keep their quarry alive, to the extent that the creatures they once wished to protect now bear little resemblance to the current population.

There's plenty of further reading on the matter, with Mark himself writing 22 articles so far on the matter in his weekly Magic column. It isn't perfect, but in writing especially, you can generally take any group of 5 characters and say which one is the Green one, the Blue one, the Red one, the Black one, and the White one. It's something that tends to happen naturally even without knowing the color pie. This just puts a little science behind that natural phenomenon.